ISO/TR 25439:2025

Technical
Report
ISO/TR 25439
First edition
Design examples of concrete-
2025-12
filled steel tubular (CFST) hybrid
structures in accordance with ISO
Exemples de conception de structures hybrides en tubes d'acier
remplis de béton (CFST) conformément à l'ISO 16521
Reference number
© ISO 2025
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ii
Contents Page
Foreword .v
Introduction .vi
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Design examples of trussed CFST hybrid structures . 1
4.1 General requirements .4
4.1.1 Match of materials (ISO 16521:2024, 5.2.6) .4
4.1.2 Requirements of CFST chords (ISO 16521:2024, 7.1) .4
4.1.3 Requirements of webs (ISO 16521:2024, 15.2.4) . .5
4.2 Calculation of indices for cross-sections .5
4.2.1 Strength (ISO 16521:2024, 10.3.1) .5
4.2.2 Stiffness (ISO 16521:2024, 10.3.2) .6
4.3 Calculation of structural resistances .7
4.3.1 Resistance in axial compression (ISO 16521:2024, 11.2.1) .7
4.3.2 Bending resistance (ISO 16521:2024, 11.2.2) .9
4.3.3 Resistance in combined compression and bending (ISO 16521:2024, 11.2.3) .10
4.3.4 Resistances of CFST chords (ISO 16521:2024, 11.2.4) .11
4.3.5 Resistances of webs (ISO 16521:2024, 11.2.5) .18
4.3.6 Shear resistances (ISO 16521:2024, 11.3) .19
4.4 Protective design . .19
4.4.1 Corrosion resistance (ISO 16521:2024, 14.2.2) .19
4.4.2 Impact resistance (ISO 16521:2024, 14.4) .21
4.5 Design of connections . 22
4.5.1 General requirements (ISO 16521:2024, Clause 15) . 22
4.5.2 Detailing requirements (ISO 16521:2024, 15.2.7) . 22
4.5.3 Resistance of joints (ISO 16521:2024, 15.2.7) . 23
4.5.4 Fatigue design calculation (ISO 16521:2024, 15.5) . 23
4.6 Calculation of core concrete void ratio (ISO 16521:2024, 16.3.10) .24
5 Design examples of concrete-encased CFST hybrid structures .24
5.1 General requirements . 26
5.1.1 Match of materials (ISO 16521:2024, 5.2.6) . 26
5.1.2 Requirements of CFST chords (ISO 16521:2024, 7.1.1) .27
5.2 Calculation of indices for cross-sections . 28
5.2.1 Strength (ISO 16521:2024, 10.3.1) . 28
5.2.2 Stiffness (ISO 16521:2024, 10.3.2) . 28
5.3 Calculation of structural resistances . 30
5.3.1 Resistance to compression (ISO 16521:2024, Clause 12) . 30
5.3.2 Resistance in combined compression and bending (ISO 16521:2024, Clause 12) .31
5.3.3 Resistance considering long-term load effects (ISO 16521:2024, 12.6) .32
5.3.4 Shear resistance (ISO 16521:2024, 12.7) . 33
5.4 Protective design for fire resistance (ISO 16521:2024, 14.3) . 36
6 Structural analysis example of concrete-encased CFST hybrid arch .36
6.1 Description of the arch structure . 36
6.2 Load conditions .37
6.3 Establishment of the fibre model . 38
6.3.1 Fibre mesh refinement . 38
6.3.2 Stress-strain relationships for steel and concrete (ISO 16521:2024, 10.2) . 38
6.4 Analysis of load-displacement relationship . 39
6.5 Analysis of deformation . 40
6.6 Analysis of stress in steel and concrete . 40

iii
Annex A (informative) Experimental verifications of design methods for concrete-filled steel
tubular (CFST) hybrid structures .42
Bibliography .64

iv
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
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The procedures used to develop this document and those intended for its further maintenance are described
in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the different types
of ISO documents should be noted. This document was drafted in accordance with the editorial rules of the
ISO/IEC Directives, Part 2 (see www.iso.org/directives).
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This document was prepared by Technical Committee ISO/TC 71, Concrete, reinforced concrete and pre-
stressed concrete, Subcommittee SC 9, Steel-concrete composite and hybrid structures.
A list of all parts in the ISO/TR 25439 series can be found on the ISO website.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.

v
Introduction
This document provides informative design examples of concrete-filled steel tubular (CFST) hybrid
structures in accordance with ISO 16521, Design of concrete-filled steel tubular (CFST) hybrid structures.
ISO 16521 stipulates the conceptional design, refined analysis method, simplified design formulae based on
refined analysis and experimental verifications, and detailing design of CFST hybrid structures. Detailed
calculations are provided in the design examples and the corresponding reference subclauses in ISO 16521
are indicated.
For trussed CFST hybrid structures, four design examples are provided, which include a three-chord
structure and two four-chord structures without concrete slab, and a four-chord structure with a concrete
slab. General requirements are verified and indices for cross-sections are calculated. The resistances of the
hybrid structures as well as the CFST chords in compression, bending, combined compression and bending,
and shear, are calculated in accordance with ISO 16521:2024, Clause 11. The protective design of corrosion
resistance and impact resistance is presented in accordance with ISO 16521:2024, Clause 14. The detailing
requirements and the resistances of the joints are verified in accordance with ISO 16521:2024, Clause 15.
Finally, the verification of the limiting value of the core concrete void in the steel tube is carried out in
accordance with ISO 16521:2024, Clause 16.
For concrete-encased CFST hybrid structures, four design examples are presented, i.e., a single-chord
structure, a six-chord structure, and a four-chord structure with circular CFST members and a four-chord
structure with rectangular CFST members. General requirements are verified and indices for cross-sections
are calculated. Resistances in compression, combined compression and bending, resistance considering
long-term load effects, shear resistance, are verified in accordance with ISO 16521:2024, Clause 12. Fire
resistance is calculated in accordance with ISO 16521:2024, Clause 14.
Clause 6 of this document presents a global structural analysis example. A concrete-encased CFST hybrid
arch structure is analysed in accordance with ISO 16521:2024, Clause 10, which employs a fibre-based
model. It includes the determination of load, model establishment, load-displacement relationship analysis,
deformation analysis, and stress and strain analysis.
Annex A is provided in this document to present some experimental data on CFST hybrid structures. These
published experimental data serve as an important basis for the development of ISO 16521. Furthermore,
they provide verifications of the design methods of CFST hybrid structures and examples for design of the
structures based on experimental data, as stipulated in the standard.
It is worth pointing out that the design examples are only provided to help readers in using ISO 16521 and
they are not based on any specific engineering projects.

vi
Technical Report ISO/TR 25439:2025(en)
Design examples of concrete-filled steel tubular (CFST) hybrid
structures in accordance with ISO 16521
1 Scope
This document provides design examples of concrete-filled steel tubular (CFST) hybrid structures in
accordance with ISO 16521.
This document includes the design calculation of major structural types in ISO 16521, i.e., trussed CFST
hybrid structures, concrete-encased CFST hybrid structures. The design examples cover the major loading
cases for the structures and follow the design procedure presented in ISO 16521:2024, Clause 6.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content constitutes
requirements of this document. For dated references, only the edition cited applies. For undated references,
the latest edition of the referenced document (including any amendments) applies.
ISO 16521, Design of concrete-filled steel tubular (CFST) hybrid structures
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 16521 apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
4 Design examples of trussed CFST hybrid structures
In this clause, the design of four examples of trussed concrete-filled steel tubular (CFST) hybrid structures
with and without a concrete slab are conducted in accordance with the corresponding clauses of ISO 16521.
The general design and construction procedure in ISO 16521:2024, 6.1, is followed, and the correspondence
between this clause and the detailed clauses of ISO 16521:2024 are shown in Table 1.
Table 1 — Design and construction procedure of trussed CFST hybrid structures
Procedure Clause in ISO 16521:2024 Subclause in this document
Preliminary structural design Clauses 5 to 8 4.1
Definition of actions (loads) Clause 9 /
Structural analysis Clause 10 4.2
Ultimate limit states design Clause 11 4.3
Serviceability limit states design Clause 13 /
Protective design Clause 14 4.4
Detailing design Clause 15 4.1 and 4.5
Construction and acceptance Clause 16 4.6

Four examples are designed as shown in Table 2. Circular (Examples T1, T2, T4) and square (Example T3)
steel tubes are used for the CFST chords and circular steel tubes are used as the webs, and the interval
lengths of the chords l (Figure 13 in ISO 16521) are 3 000 mm, 7 750 mm, 7 750 mm, and 3 000 mm for the
four examples respectively.
Table 2 — Geometric and material properties of design examples
Chords in com-
Chords in tension Web
Example pression D×t or h (mm) b (mm) f (MPa) f (MPa)
i i y ck
D×t or B×t (mm) d ×t (mm)
w w
B×t (mm)
T1 D×t, 720×20 D×t, 720×20 392×18 2 000 2 000 355 41
T2 D×t, 1 400×30 D×t, 1 400×30 850×18 8 500 8 500 420 60
T3 B×t, 1 400×40 B×t, 1 400×40 850×18 8 500 8 500 420 60
T4 D×t, 400×10 D×t, 700×25 280×14 1 875 1 875 355 41
NOTE D is the outside diameter of the circular CFST member, B is the width of the square CFST member, t is the wall thickness of
the steel tube of the CFST member, d is the outside diameter of the web, t is the wall thickness of the steel tube of the web, h
w w i
is the distance along the cross-sectional height between the centroids of compression and the tension chords, b is the distance
i
between the centre points of chords out of the plane of bending moment, f is the characteristic yield strength of steel, f is the
y ck
characteristic compressive cylinder strength of concrete.
Among them, Example T1 is a three-chord trussed CFST hybrid structures without a concrete slab and
with circular CFST members (Figure 1); Example T2 and Example T3 are four-chord trussed CFST hybrid
structures without a concrete slab and with circular and square CFST members, respectively (Figure 2 and
Figure 3); Example T4 is a four-chord trussed CFST hybrid structure with a concrete slab and with circular
CFST members (Figure 4).
For example T4, the characteristic compressive strength of concrete slab is 33 MPa, and the thickness h is
b
150 mm. Other dimensions (shown in Figure 4) are: b = 1 300 mm, b = 900 mm, b = 950 mm. Twenty-five
f t m
longitudinal reinforcement bars with a diameter of 25 mm are uniformly distributed in the concrete slab.
The thickness of the concrete cover is 35 mm.
Key
1 CFST chords
2 webs
Figure 1 — Cross-section of three-chord trussed CFST hybrid structure with circular CFST members
(Example T1)
Key
1 CFST chords
2 webs
Figure 2 — Cross-section of four-chord trussed CFST hybrid structure with circular CFST members
(Example T2)
Key
1 CFST chords
2 webs
Figure 3 — Cross-section of four-chord trussed CFST hybrid structure with circular CFST members
(Example T3)
Key
1 CFST chords in tension
2 CFST chords in compression
3 webs
4 concrete slab
5 concrete encasement
Figure 4 — Cross-section of four-chord trussed CFST hybrid structure with a concrete slab and
circular CFST members (Example T4)
4.1 General requirements
4.1.1 Match of materials (ISO 16521:2024, 5.2.6)
As shown in Table 3, the four examples meet the requirements of ISO 16521:2024, 5.2.6, for the match
relationships between the steel tubes and their core concrete. Other requirements of material strength in
ISO 16521:2024, Clause 5, are also checked and confirmed for the four examples.
Table 3 — Match of materials
Characteristic yield strength of steel tube f
Characteristic strength of core concrete f
y
ck
Example
(MPa)
(MPa)
T1 355 41
T2 420 60
T3 420 60
T4 355 41
4.1.2 Requirements of CFST chords (ISO 16521:2024, 7.1)
The outside diameters of the steel tubes in the four examples are greater than 200 mm and their wall
thicknesses are greater than 4 mm, which meet the requirements of ISO 16521:2024, 7.1.1.1 and 7.1.1.2. The
outside diameter-to-thickness ratios (D/t) or width-to-thickness ratios (B/t), cross-sectional steel ratios (α ),
s
and confinement factors (ξ) of the CFST chords are also checked in Table 4, which satisfy the requirements
of ISO 16521:2024, 7.1.1.3, 7.1.1.4 and 7.1.1.5.

Table 4 — General requirements check of CFST chords
Outside diameter-to-
Cross-sectional steel ratio
thickness ratio D/t or Confinement factor ξ
α
Example
s
width-to-thickness ratio B/t
Value Limiting value Value Limit value Value Limiting value
T1 36,0 16,6 to 99,3 0,12 1,33
0,06 to 0,23 0,6 to 4,0
T2 46,7 14,0 to 83,9 0,09 0,87
T3 35,0 7,5 to 48,6 0,12 0,10 to 0,23 1,18 1,0 to 4,0
T4 (chords in compression) 40,0 16,6 to 99,3 0,11 1,18
0,06 to 0,23 0,6 to 4,0
T4 (chords in tension) 28,0 16,6 to 99,3 0,16 1,70
NOTE Steel ratio (α ) as defined in ISO 16521:2024, 7.1.1.5, is the ratio of the cross-sectional area of the hollow steel tube to the
s
cross-sectional area of the core concrete. Confinement factor (ξ) as defined in ISO 16521:2024, 3.6, is the ratio of the nominal
compressive strength of cross-section of the steel tube to that of the core concrete in a CFST member.
4.1.3 Requirements of webs (ISO 16521:2024, 15.2.4)
The requirements of ISO 16521:2024, 15.2.4, regarding the geometric parameters of the webs are checked,
as shown in Table 5.
Table 5 — Ratios of steel tubular webs
l /h A /A
1 i w s
Example
Value Limiting value Value Limiting value
T1 1,5 0,48
T2 0,9 0,36
≤ 4,0 ≥ 0,2
T3 0,9 0,28
T4 1,6 0,22
NOTE l and h are the distance between the centroids of horizontal webs and the distance between the centroids of chords,
1 i
respectively. A and A are the cross-sectional area of the hollow steel tubular web and the cross-sectional area of the single
w s
chord, respectively.
4.2 Calculation of indices for cross-sections
Both the strength and stiffness indices for cross-sections of the four examples are calculated in 4.2 in
accordance with ISO 16521:2024, 10.3.
4.2.1 Strength (ISO 16521:2024, 10.3.1)
The CFST chord of Example T1 is taken as an example:
The characteristic compressive strength of CFST cross-section f [Formula (64) of ISO 16521:2024],
scy
the design compressive strength f [Formula (63) of ISO 16521:2024], and the design shear strength f
sc sv
[Formula (65) of ISO 16521:2024] are calculated as follows:
ff11,,41 02

scycc k
11,,41 0213, 3407, 9 1 (1)
 80,86 MPa
f
scy
f 
sc

msc
80,86
= (2)
14, 0
 57,76 MPa
23,,30 134
ff0,,422 0 313

sv ssc
23, 3 0,134
0,,422 0 31301,,21 333 57,76 (3)

 25,46 MPa
where, α is the strength adjustment coefficient as defined in ISO 16521:2024, 7.1.1.6. γ is taken as 1,40 in
c msc
accordance with ISO 16521:2024, 10.3.1.1.
The design strength indices of CFST cross-sections for each example are summarized in Table 6.
Table 6 — Design values of strength indices of CFST chords
CFST chord
Example
f (MPa) f (MPa)
sc sv
T1 57,76 25,46
T2 64,17 26,64
T3 69,23 32,99
T4 (upper chords) 54,32 23,55
T4 (lower chords) 66,54 30,46
4.2.2 Stiffness (ISO 16521:2024, 10.3.2)
Example T1 is taken as an example.
Elastic compression stiffness (EA) [Formula (70) of ISO 16521:2024], elastic tension stiffness (EA)
c,h t,h
[Formula (71)], elastic flexural stiffness (EI) [Formula (72) of ISO 16521:2024], and elastic shear stiffness
h
(GA) [Formula (73) of ISO 16521:2024] of the cross-section of the trussed CFST hybrid structure are
h
calculated as follows:
EA EA EA EA EA
 
ss s,ll c,cc c,oc oc

c,h
3 206 00043982 28 8144363168 (4)

58, 610 kN
EA EA EA
 ss s,ll
t,h
3 206 00043982 (5)

27, 210 kN
EI EI EI EI EI
ss ,,hs ll ,,hc cc ,,hc oc oc ,h
h
110 10
2 206 00022, 210 206 000 80, 91 0

(6)
11 11
2128 814,,72 10 28 814 6561 0

7 2
54, 610 kNm
GA GA GA GA
 
 ss cc,,cc oc oc
h
37923143982 12006363168 (7)
23, 510 kN
where the modulus of elasticity, Poisson’s ratio, and shear modulus of the steel are taken as 2,06×10 MPa,
0,3, and 79 231 MPa, respectively; the modulus of elasticity, Poisson’s ratio and shear modulus of the core
concrete are taken as 28 814 MPa, 0,2 and 12 006 MPa, respectively.
The calculation results of each example are summarized in Table 7.
Table 7 — Stiffness values of trussed CFST hybrid cross-sections
Example (EA) (kN) (EA) (kN) (EI) (kN·m ) (GA) (kN)
c,h t,h h h
7 7 7 7
T1 5,86×10 2,72×10 5,46×10 2,35×10
8 8 9 8
T2 3,03×10 1,06×10 5,52×10 1,23×10
8 8 9 8
T3 4,22×10 1,79×10 7,72×10 1,70×10
8 7 6 7
T4 1,00×10 2,69×10 4,69×10 4,09×10
4.3 Calculation of structural resistances
The design processes for the ultimate limit states of trussed CFST hybrid structures are presented. The
resistances of the global structures (4.3.1) as well as their chords and webs (4.3.2 and 4.3.3) are both
calculated.
4.3.1 Resistance in axial compression (ISO 16521:2024, 11.2.1)
In accordance with ISO 16521:2024, 11.2.1, the resistances in axial compression of the trussed CFST hybrid
structures without a concrete slab, i.e., Example T1, Example T2 and Example T3, are calculated.
Geometric parameters: The longitudinal lengths L of the trussed CFST hybrid structures in Example T1,
Example T2 and Example T3 are 40 000 mm, 223 784 mm and 223 784 mm, respectively.
Example T1 is taken as an example for calculation:
Step 1: Calculation of the equivalent slenderness ratio
Through a global structural analysis, the equivalent slenderness ratio of the trussed CFST hybrid structure
is determined as 76,53.
Step 2: Calculation of the stability factor φ
In accordance with ISO 16521:2024, 11.2.1, the stability factor φ for the trussed CFST hybrid structure in
axial compression is determined.
Critical slenderness ratio for the elasto-plastic buckling [Formula (84) of ISO 16521:2024]:

420 550

o
10,,21 14 f
c ck
42013, 3 550
 (8)
10,,21133 ,14 07, 941
11,63
Critical slenderness ratio for the elastic buckling [Formula (83) of ISO 16521:2024]:
 
p
f
y
 (9)
92,51
03,
00, 5
  
235  25  
 
s
d 13000 4657ln
  
 
 
 
ff 50,1
 
  
ycc k
  
03,,005
235 25 01, 2
      
13000 4657ln   (10)
     
 
355 07, 9415 01,
      
9908,52
d
e
 35

p
9913,07
 (11)
92,5135

3
47, 81 0
1352 e

p 0
a


po
3
135292,,51 11 63  47, 810

 (12)
992,,5111 63

7
59, 610
be2a
p
37
47,,8105299610 25, 1 (13)
3
48, 910
ca1 b
oo
72 3
1159,,64011631 ,,89 01 163 (14)

10, 6
The equivalent slenderness ratio of the trussed CFST hybrid structure λ is greater than λ and less than λ ,
o p
so the stability factor φ [Formula (77) of ISO 16521:2024]:
abc
72 3
59,,61076534(,89 10 ),76 53 10, 6 (15)
06, 9
Step 3: Calculation of the resistance
In accordance with ISO 16521:2024, 11.2.1, the resistance of the trussed CFST hybrid structure can be
calculated.
Resistance of the cross-section of a single CFST chord to compression [Formula (75) of ISO 16521:2024]:
Nf A
cscsc
57,76 407150 (16)
23, 5k10 N
where A is the cross-sectional area of a single CFST chord.
sc
Resistance of the trussed CFST hybrid structure in axial compression [Formula (74) of ISO 16521:2024]:
NN=
uc
=0,,6932 3510 (17)
48, 6 10 kN
Similarly, the resistances of the trussed CFST hybrid structure in Example T2 and Example T3 in axial
5 5
compression are determined as 1,61×10 kN and 2,15×10 kN, respectively.
4.3.2 Bending resistance (ISO 16521:2024, 11.2.2)
In accordance with ISO 16521:2024, 11.2.2, the bending resistances of the trussed CFST hybrid structures
with and without a concrete slab, i.e., Examples T1-T4, are calculated.
Example T1 is taken as an example for calculation:
1) Trussed CFST hybrid structure without a concrete slab
Resistance of the cross-section of a single CFST chord to tension [Formula (95) of ISO 16521:2024]:

Nf11, 04,  A
ts s
11, 04,,012 308,70 43982 (18)

14, 310 kN
where the design strength of steel f is taken as 355/1,15 = 308,70 MPa.
Bending resistance of the trussed CFST hybrid structure without a concrete slab [Formula (94) of
ISO 16521:2024]:
MN min, Nh

uc ti
=min,486410 ,,29 10 2 (19)

85, 810 kNm
Similarly, the bending resistances of the trussed CFST hybrid structure in Example T2 and Example T3 are
6 6
determined as 1,37×10 kN·m and 1,83×10 kN·m, respectively.
2) Trussed CFST hybrid structure with a concrete slab
For the trussed CFST hybrid structure with a concrete slab, the position of the neutral axis is determined
first.
As stipulated in ISO 16521:2024, 11.2.2.3, the resistance of the concrete slab in axial compression N is
slab
calculated in accordance with relevant national standards. In this example, the resistance is calculated as
the summation of the resistances of the concrete and the compression longitudinal reinforcement, with the
stability factor (φ ) considered, i.e., Nb hf Af'' , where A ' and f ' are the cross-sectional

c slab ce bc ll l l
area and design strength of the compression longitudinal reinforcement. The value of φ is determined as
c
0,75. The effective width of the concrete slab corresponding to the single chord (b ) is determined as
e
2 500 mm.
The stability factor of the chord in compression φ = 0,94 is calculated by the same method as in
sc
ISO 16521:2024, 11.2.1.
 
bh fA ''ff  A
cebc ll sc sc sc
 
07, 522500 15022 25490,,63347,83
(20)
15, 6101kN < ,,10- 4 fA
ss
33, 910 kN
Therefore, the neutral axis of the cross-section is determined to be within the height of the webs.
Consequently, the bending resistance is calculated in accordance with the schematic diagram given by
Figure 13 in ISO 16521:2024, 11.2.2.3.
Mb hf Af'' hD22hf Ah

uc eb csll tb cscsc i

 
07, 5225000150 2225 490,,63347 83 2250 09,,454322125600 1 875 (21)
59, 110 kNm
where h is the height of the cross-section of the trussed CFST hybrid structure with a concrete slab, which is
taken as 2 675 mm.
4.3.3 Resistance in combined compression and bending (ISO 16521:2024, 11.2.3)
In accordance with ISO 16521:2024, 11.2.3, the resistance of the trussed CFST hybrid structure without a
concrete slab in combined compression and bending is calculated.
Load definitions and geometric parameters: The factored axial compression N = 20 000 kN, the initial
deflection of the structure u = 100 mm, the distances between the centre points of end cross-sections (L in
Figure 14 of ISO 16521:2024) of Example T1, Example T2 and Example T3 are 40 000 mm, 223 784 mm and
223 784 mm, respectively.
Example T1 is taken as an example for calculation:
Distance from the cross-sectional centre of gravity to the centroidal axis of the chord in the compression
zone (r in Figure 14 of ISO 16521:2024) [Formula (98) of ISO 16521:2024]:
c
N
uc2
r  hi
c
NN
uc1uc2
2000 (22)
 666,67 mm
Distance from the cross-sectional centre of gravity to the centroidal axis of the chord in the tension zone (r
t
in Figure 14 of ISO 16521:2024) [Formula (99) of ISO 16521:2024]:
N
uc1
r  hi
t
NN
uc1uc2
2000 (23)
 1333,33 mm
Axial force corresponding to the equilibrium point of the N-M correlation curve [Formula (96) of
ISO 16521:2024]:
NN N
Bc t

 06,,92()235101,4310 (24)
18, 110 kN
Bending moment corresponding to the equilibrium point of tension and compression boundary in resistance
N-M correlation curve [Formula (97) of ISO 16521:2024]:
MN rN r
Bcct t
=0,,692123510 666,,6743 10 1333,33 10000 (25)

40, 710 kNm
Euler's critical force calculated from the equivalent slenderness ratio [Formula (101) of ISO 16521:2024]:
NEA
E 
c
29 10 2
 2188,,010105 0 76,53 (26)

65, 010 kN
Factored bending moment caused by the initial bending of the structure [Formula (104) of ISO 16521:2024]:
MN u
2000001, (27)
2000kN m
M M
B
Since u 01, mm 21, 8 , verify the resistance in combined compression and bending in
N N
B
accordance with Formula (100) of ISO 16521:2024:

N M

WN1 /Nf
fA 
sc Esc
sc sc
3 3
2000010 22000010 100
  (28)
87 7
06,,9357 76 407150  
84,,4101069210 / 65,,01 05 770
 
 
04, 61
Thus, Example T1 satisfies the requirements of the resistance of the trussed CFST hybrid structure in
combined compression and bending.
Similarly, Example T2 and Example T3 also satisfy the requirements of the resistance of the trussed CFST
hybrid structure in combined compression and bending.
4.3.4 Resistances of CFST chords (ISO 16521:2024, 11.2.4)
The resistances of each chord in trussed CFST hybrid structures are also calculated. In accordance with
ISO 16521:2024, 11.2.4, the resistances of chords are calculated in various individual loads and combined
loads, which are axial tension, axial compression, bending, combined compression and bending, combined
tension and bending, shear, torsion, combined compression and torsion, combined compression bending and
torsion, combined compression, bending and shear, and combined compression, bending, torsion and shear.

Factored loads for the verifications are set as follows:
Combined compression and bending: Factored axial compression N = 5 000 kN, factored bending moment M
= 500 kN·m.
Combined tension and bending: Factored axial tension N = 4 000 kN, factored bending moment M = 500 kN·m.
Combined compression and torsion: Factored axial compression N = 9 000 kN, factored torsional moment T
= 1 000 kN·m.
Combined compression, bending, and torsion: Factored axial compression N = 4 000 kN, factored bending
moment M = 500 kN·m, factored torsional moment T = 1 000 kN·m.
Combined compression, bending, and shear: Factored axial compression N = 4 000 kN, factored bending
moment M = 500 kN·m, shear force V = 2 000 kN.
Combined compression, bending, torsion, and shear: Factored axial compression N = 4 000 kN, factored
bending moment M = 500 kN·m, factored torsional moment T = 1 000 kN·m, factored shear force V = 2 000 kN.
1) Resistances in axial compression and axial tension
The CFST chord of Example T1 is taken as an example. The resistances in axial compression and tension of
the chord [Formulae (105) and (106) of ISO 16521:2024] are calculated respectively as follows:
N 09,,82 3510
c
(29)
23, 010 kN
N 14, 310 kN (30)
t
where the parameters for the calculation of the stability factor φ are listed in Table 8.
Table 8 — Parameters for calculation of resistance in axial compression
Parameter λ λ λ a b c d e
0 p
-7 -3 -3
Value 11,63 92,51 15 -5,96×10 -4,89×10 1,06 9 913,07 -4,78×10
Similarly, it can be calculated that the resistances in axial compression and tension of a single chord in
4 4
Example T2 are 9,88×10 kN and 5,01×10 kN, respectively, and the resistances in axial compression and
5 4
tension of a single chord in Example T3 are 1,36×10 kN and 8,34×10 kN, respectively.
2) Bending resistance
The CFST chord of Example T1 is taken as an example. The section modulus of the chord [Formula (110)
of ISO 16521:2024] and the plastic development factor of the bending resistance [Formula (109) of
ISO 16521:2024]:
D
W 
sc1
 720 /32 (31)
36, 6 10 mm
11,,0480ln() ,1
m
11,,0481ln(),,33 01 (32)
12, 7
Bending resistance of the CFST chord [Formula (108) of ISO 16521:2024]:
MW f
cu msc1 sc
12,,7 3661 05 77, 6 (33)

26, 8 10 kNm
Similarly, the bending resistances of a single chord in Example T2 and Example T3 are 1,87×10 kN·m and
3,67×10 kN·m, respectively.
3) Resistance in combined compression and in-plane bending
The CFST chord of Example T1 is taken as an example.
Step 1: Calculation of the resistance of the cross-section
08, 4
01,,014
08, 4
01,,0141 ,33 (34)
02, 1
11, 5
10,18
11, 5
10,,18133 (35)
11, 3
21() 
c

21(),13 1
 (36)
02, 1
12, 4
1
b

11 ,13
 (37)
02, 1
29, 5
a12
1202, 1 (38)
05, 8
NN/,0212 , so the resistance of the cross-section is verified in accordance with Formula (112)
cd c0
of ISO 16521:2024.
6 66
29, 5510 12, 4510
 
bN cN M
51 0
cd cd cd
    00, 61 (39)
2 2 7 9
N M
N 23,,51 0 2681 0
c cu
c 23, 51 0

Resistance of the cross-section satisfies the requirements.

Step 2: Calculation of the resistance of the single CFST chord
21() 
c

21(),13 1
 (40)
02, 1
12, 4
NEA cc

cE
 1,956 10
 (41)
85, 810 kN
 
Ncd
d 10,4
 
N
 cE 
 
51 0
10,4 (42)
 
 
85, 8101000
 
10, 0
1
b
 
11 ,13
 (43)
00,,98  21
31, 3
a12
1209,,80 21 (44)
06, 0
Since NN/,0212 , the resistance is verified in accordance with Formula (119) of ISO 16521:2024:
cd c0
6 6
31, 3510 12, 45110
 
bN cN M
1 1 51 0
cd cd cd
   
2 2 7 9
Nd M 7 10, 0 (45)
N 23, 51 0 26, 61 0
c cu
c 23, 51 0

00, 7 1
The resistance of the single CFST chord in combined compression and in-plane bending satisfies the
requirements.
Similarly, for Example T2 and Example T3, the resistances of a single chord in combined compression and in-
plane bending satisfy the requirements, respectively.
4) Resistance in combined tension and in-plane bending
The CFST chord of Example T1 is taken as an example [Formula (125) of ISO 16521:2024]:
6 8
Ntd Mcd 41 0 551 0
 
11,,--04 fA M 11,,0401,,2 308 70 43982 (46)
 
26, 61 0
ss cu
04, 71
The resistance in combined tension and in-plane bending of the single CFST chord satisfies the requirements.

Similarly, the resistances in combined tension and in-plane bending of a single chord in Example T2 and
Example T3 satisfy the requirements, respectively.
5) Shear resistance
The CFST chord of Example T1 is taken as an example [Formulae (127)-(128) of ISO 16521:2024].
09,,70 2ln
v
09,,70 21ln ,33 (47)
10, 3
VA f
cu vscsv
10,,3 40715025 46 (48)
10, 710kN
Similarly, the shear resistances of a single chord in Example T2 and Example T3 are 3,86×10 kN and
5,78×10 kN, respectively.
6) Torsional resistance
The CFST chord of Example T1 is taken as an example [Formulae (130)-(132) of ISO 16521:2024].
D
W 
sc,t
720
 (49)
73, 3 10 mm
1,,294 0 267ln
t
1,,294 0 267ln13, 3 (50)
13, 7
TW f
cu tsc,tsv
13,,77 3310 25,46 (51)

25, 610 kNm
Similarly, it can be calculated that the torsional resistances of a single chord in Example T2 and Example T3
4 4
are 1,80×10 kN·m and 2,52×10 kN·m, respectively.
7) Resistance in combined compression and torsion
The CFST chord of Example T1 is taken as an example.
Step 1: Calculation of the resistance of the cross-section [Formula (133) of ISO 16521:2024]
24, 2
24, 2
6 9
N T    
    91 0 10
cd cd
  
 
 
   
 7   9 
(52)
N T
    23, 51 0 2,,5510
c cu
   
02, 51
Step 2: Calculation of the resistance of the chord [Formula (134) of ISO 16521:2024]
2,44 2
24, 2
6 9
   
 N  T 
91 0 10
cd cd
 = 
   
   
   
7 9
(53)
N T
09,,8235 10 25, 51 0
 c   cu 
   
=02, 61
Resistance of the single CFST chord in combined compression and torsion satisfies the requirements.

Similarly, the resistances of a single chord in compression and torsion in Example T2 and Example T3 satisfy
the requirements, respectively.
8) Resistance in combined compression, bending and torsion
The CFST chord in Example T1 is taken as an example.
N
 
cd
d 10,4
 
N
 
cE
 
41 0
10,4 (54)
 
 8 
85, 61 0
 
10, 0
T
cd
 
T
(55)
cu
03, 9
0,417
1 

e 0
0,417
10,,39 113 (56)

10, 5
0,417
1 

e 0
0,417
10,39 02, 1 (57)

02, 0
21() 
e
c

e
21,051
 (58)
02, 0
05, 0
1
e
b
 
e
11 ,05
 (59)
09,,80 20
13, 3
a12
1209,,80 21 (60)
06, 0
NN 4102/,3510
cd c
04, 177
(61)
 
T
 
3 cd
01, 72 1  03, 7
0  
T
 
 
cu
 
Hence, the resistance is calculated in combined compression, bending, and torsion in accordance with
Formula (136) of ISO 16521:2024.
24,
2 2
 
N N M T
    1  
cd cd cd cd
b c   
     
N Nd M T
 
     
c c cu cu
 
24,
2 2
 6 6 8  9
   
41 0 41 0 1 551 0 11 0
 
13, 3 05, 0   (62)
   
   
7 7 9 9
10, 0
 
23, 51 0 23, 51 0 26,,61 0 2551 0
   
 
01, 61
Resistance in combined compression, bending, and torsion satisfies the requirements.
Similarly, the resistances of a single chord in combined compression, bending, and torsion in Example T2
and Example T3 satisfy the requirements, respectively.
9) Resistance in combined compression, bending, and shear
The CFST chord of Example T1 is taken as an example.

NN 4102/,3510
cd c
04, 177
(63)
 
V 
3 cd
 
01, 72 1 03, 9
 
V
 
 cu 
 
The resistance is calculate
...